A property of holomorphic functions related to plurisubharmonic functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914954047651840 |
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| author | Van Phu, Nguyen |
| author_facet | Van Phu, Nguyen |
| contents | Let $φ$ be a negative plurisubharmonic function in a pseudoconvex domain $Ω$ in $\mathbb{C}^{n}$ and $f$ be a bounded holomorphic function belonging to $L^{2}(Ω, φ)$. For all negative plurisubharmonic functions $ψ$ satisfying that $ψ$ is close to $φ$ in the $L^1(Ω)$ norm. Using the recent results about $L^2-$estimate for $\overline{\partial}-$equation and strong openness conjecture, we prove that there exists a holomorphic function $g$ belonging to $L^{2}( Ω, ψ)$ such that $g$ is close to $f$ in the $L^2$ norm on some relatively compact open subset $Ω^{'}$ of $Ω.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12296 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A property of holomorphic functions related to plurisubharmonic functions Van Phu, Nguyen Complex Variables Functional Analysis 32U05, 32U15, 32W05 Let $φ$ be a negative plurisubharmonic function in a pseudoconvex domain $Ω$ in $\mathbb{C}^{n}$ and $f$ be a bounded holomorphic function belonging to $L^{2}(Ω, φ)$. For all negative plurisubharmonic functions $ψ$ satisfying that $ψ$ is close to $φ$ in the $L^1(Ω)$ norm. Using the recent results about $L^2-$estimate for $\overline{\partial}-$equation and strong openness conjecture, we prove that there exists a holomorphic function $g$ belonging to $L^{2}( Ω, ψ)$ such that $g$ is close to $f$ in the $L^2$ norm on some relatively compact open subset $Ω^{'}$ of $Ω.$ |
| title | A property of holomorphic functions related to plurisubharmonic functions |
| topic | Complex Variables Functional Analysis 32U05, 32U15, 32W05 |
| url | https://arxiv.org/abs/2311.12296 |